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Linear interpolation and joint model fitting of experimental transiograms for Markov chain simulation of categorical spatial variables

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Abstract:

In Markov chain random field (MCRF) simulation of categorical spatial variables with multiple classes, joint modeling of a large number of experimental auto and cross-transiograms is needed. This can be tedious when mathematical models are used to fit the complex features of experimental transiograms. Linear interpolation can be used to perform the joint modeling quickly regardless of the number and the complexity of experimental transiograms. In this paper, we demonstrated the mathematical validity of linear interpolation as a joint transiogram-modeling method, explored its applicability and limitations, and tested its effect on simulated results by case studies with comparison to the joint model-fitting method. Simulations of a five-class variable showed little difference in patterns for interpolated and fitted transiogram models when samples were sufficient and experimental transiograms were in regular shapes; however, they neither showed large difference between these two kinds of transiogram models when samples were relatively sparse, which might indicate that MCRFs were not much sensitive to the difference in the detail of the two kinds of transiogram models as long as their change trends were identical. If available, expert knowledge might play an important role in transiogram modeling when experimental transiograms could not reflect the real spatial variation of the categorical variable under study. An extra finding was that class enclosure feature (i.e., a class always appears within another class) was captured by the asymmetrical property of transiograms and further generated in simulated patterns, whereas this might not be achieved in conventional geostatistics. We conclude that (i) when samples are sufficient and experimental transiograms are reliable, linear interpolation is satisfactory and more efficient than model fitting; (ii) when samples are relatively sparse, choosing a suitable lag tolerance is necessary to obtain reliable experimental transiograms for linear interpolation; (iii) when samples are very sparse (or few) and experimental transiograms are erratic, coarse model fitting based on expert knowledge is recommended as a better choice whereas both linear interpolation and precise model fitting do not make sense anymore.

Keywords: Markov chain random field; categorical spatial variable; expert knowledge; transiogram

Document Type: Research Article

DOI: https://doi.org/10.1080/13658810903127991

Affiliations: 1: Key Laboratory of Subtropical Agriculture Resource and Environment, Ministry of Agriculture, College of Resource and Environment, Huazhong Agricultural University, Wuhan, Hubei, China,Department of Resource and Environmental Information Science and Engineering, Huazhong Agricultural University, Wuhan, Hubei, China,Department of Geography and Center for Environmental Sciences and Engineering, University of Connecticut, Storrs, CT, USA 2: Department of Geography and Center for Environmental Sciences and Engineering, University of Connecticut, Storrs, CT, USA

Publication date: 2010-06-01

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